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Exponential Speedup of Fixed-Parameter Algorithms on K 3,3-Minor-Free or K 5-Minor-Free Graphs

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Algorithms and Computation (ISAAC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

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Abstract

We present a fixed-parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of K 5 or K 3,3 as a minor in time O(416.5√k n O(1)), which is an exponential factor faster than the previous O(2O(k)nO(1)). In fact, we present our algorithm for any H-minor-free graph where H is a single-crossing graph (can be drawn in the plane with at most one crossing) and obtain the algorithm for K 3,3(K 5)-minor-free graphs as a special case. As a consequence, we extend our results to several other problems such as vertex cover, edge dominating set, independent set, clique-transversal set, kernels in digraphs, feedback vertex set and a series of vertex removal problems. Our work generalizes and extends the recent result of exponential speedup in designing fixed-parameter algorithms on planar graphs by Alber et al. to other (nonplanar) classes of graphs.

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Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, 200 Technology Square, Cambridge, MA, 02139, USA

    Erik D. Demaine & Mohammad Taghi Hajiaghayi

  2. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord — Mòdul C5, Desp. 211b, c/Jordi Girona Salgado, 1-3, E-08034, Barcelona, Spain

    Dimitrios M. Thilikos

Authors
  1. Erik D. Demaine
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  2. Mohammad Taghi Hajiaghayi
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  3. Dimitrios M. Thilikos
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Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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Demaine, E.D., Hajiaghayi, M.T., Thilikos, D.M. (2002). Exponential Speedup of Fixed-Parameter Algorithms on K 3,3-Minor-Free or K 5-Minor-Free Graphs. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_24

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  • DOI: https://doi.org/10.1007/3-540-36136-7_24

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